The air pressure p(x,t) in an organ pipe is governed by the wave equation d 2 p 1 d 2 p n ^ t T' 0 < x < /, 0 < /, 9x2 c 2 9/2 where I is the length ofthe pipe and c is a physical constant. Ifthe pipe is open, the boundary conditions are given by p(0. t) = po and p{L t) = po. Ifthe pipe is closed at the end where x = /, the boundary conditions are /?(0, t) po and ^(/,r) = 0. 9x Assume that c = I, / = 1 and thatthe initial conditions are 3p p{x,0) = pnCos2nx, and (x,0) = 0, 0

L30 - 2 ex. Find the most general antiderivative of the following: 1) f(x)=sec xtanx 2) f(x)= e 5x n NOTE: If f(x)= x (n = ▯ −1), then F(x)= If n ≥ 0, then x If n< 0, then x −3 ex. Find F(x)f i f(x)= x . 1 ex. If f(x)= x , ﬁnd F(x).